Research on Efficient Graph Partitioning Algorithms for Sparse Matrices

For accelerating the convergence of numerical computation of sparse matrices, the classical approach is to partition sparse matrices into block-diagonal structures by graph partitioning algorithms, and then apply distinct preconditioning strategies for different blocks, which enable parallel processing of individual blocks and significantly enhances the efficiency. This paper comprehensively analyzes typical graph partitioning algorithms, including METIS, ParMETIS, hMETIS and Scotch in terms of efficiency and resource consumption. By experiments on standardized test cases, we systematically compare these algorithms and summarizes their respective characteristics and optimal application scenarios for future work.